Guided Waves in Free Space

**Chapter 7**

**Abstract**

**1. Introduction**

processing unit (CPU).

alternatives.

**101**

Study of Refraction Effects for

*Vladimir Schejbal, Ondrej Fiser and Vadim Zavodny*

This chapter investigates the radio-wave propagation above irregular ground, including the troposphere, using physical optics computation. We briefly describe used simplifications, which substantially reduce numerical simulations. Using the principle of stationary phase, we can approximate the propagation over a terrain (the PO approximation of the vector problem with a 3-D surface) with a 2-D surface. Moreover, we approximate the reflection coefficient for a surface with random deviations considering the surface standard deviation and the local Fresnel reflection coefficient for the smooth ground. We present the novel computations of physical optics for investigations of radar coverage diagrams. We consider both monostatic and bistatic radars, the far-field antenna measuring ranges, and studies of air refraction index. We validate the calculations by both experimental results and the other numerical simulations. The experimental results changed during seasons and according to terrain and troposphere conditions including vegetation,

**Keywords:** electromagnetic propagation, electromagnetic reflection, microwave

Propagation of radio waves above earth is very challenging for uncountable communication tasks comprising the radar coverage and far-field antenna measurement ranges. Several methods have been described [1–13] such as geometrical optics (GO) and various modifications of the geometrical theory of diffraction. Full wave methods are rather demanding, bearing in mind the memory and central

We present a brief description of the physical optics (PO) method [14–22] applied for irregular ground reflection considering both horizontal and vertical polarizations, electrical properties of earth (i.e., reflection coefficient), scattering of radio waves from random surfaces, and the shadow radiation. The improved computation of radio waves above uneven ground uses PO and line integrals, taking into consideration the vector problem and shadowing [18, 19]. This is a more consistent

method for low-altitude fields and diffraction zones without any additional

method (PEM) for altered environment circumstances and modifications.

We perform new numerical simulations, which we compare with ample experimental results and other numerical simulations such as the parabolic equation

Propagation over Terrain

cultivation, snow, and air temperature and pressure.

propagation, losses, radar antennas, electromagnetic refraction
